Quantitative Skills Assessment Questions
SECTION A (You should attempt all 10 questions) A1. The sample mean is an unbiased estimator for the population mean. This means:
(A) The sample mean always equals the population mean.
(B) The average sample mean, over all possible samples, equals the population mean.
(C) The sample mean is always very close to the population mean.
(D) The sample mean will only vary a little from the population mean.
A2. The central limit theorem tells us that the sampling distribution of the mean is approximately normal. Which of the following conditions are necessary for the theorem to be valid?
(A) The sample size has to be large.
(B) We have to be sampling from a normal population.
(C) The population has to be symmetric.
(D) Both (A) and (B).
A3. The average monthly mortgage payment for recent home buyers in Mississippi is µ = $732 with standard deviation of = $421. A random sample of 125 recent home buyers is selected. The approximate probability that their average monthly mortgage payment will be more than $782 is ___________.
(A) 0.4082
(B) 0.4522
(C) 0.0918
(D) 0.9082
A4. Which of the following is not a point estimate? (A) (B) (C) s (D)
A5. A sample of 100 items is taken from a population. The standard error is 839 units. If a sample of 500 items had been taken instead, what would have been the standard error?
(A) 83.9
(B) 375.2
(C) 167.8
(D) 20.0
A6. In a sample of 400 shops taken in 2005, it was discovered that 136 of them sold carpets at below the list prices which had been recommended by manufacturers. What size sample would have to be taken in order to estimate the proportion to within 0.02? (Assuming 95% confidence)
(A) 2100
(B) 2260
(C) 2158
(D) 2156
A7. Given the following hypothesis: H0 : µ = 400 H1 : µ ≠ 400
For a random sample of 12 observations, the sample mean was 407 and the standard deviation 6. Using the 5% significance level, compute the value of test statistic.
(A) 5.03
(B) 6.23
(C) 4.04
(D) 2.98
A8. A researcher wishes to determine
(A) The sample mean always equals the population mean.
(B) The average sample mean, over all possible samples, equals the population mean.
(C) The sample mean is always very close to the population mean.
(D) The sample mean will only vary a little from the population mean.
A2. The central limit theorem tells us that the sampling distribution of the mean is approximately normal. Which of the following conditions are necessary for the theorem to be valid?
(A) The sample size has to be large.
(B) We have to be sampling from a normal population.
(C) The population has to be symmetric.
(D) Both (A) and (B).
A3. The average monthly mortgage payment for recent home buyers in Mississippi is µ = $732 with standard deviation of = $421. A random sample of 125 recent home buyers is selected. The approximate probability that their average monthly mortgage payment will be more than $782 is ___________.
(A) 0.4082
(B) 0.4522
(C) 0.0918
(D) 0.9082
A4. Which of the following is not a point estimate? (A) (B) (C) s (D)
A5. A sample of 100 items is taken from a population. The standard error is 839 units. If a sample of 500 items had been taken instead, what would have been the standard error?
(A) 83.9
(B) 375.2
(C) 167.8
(D) 20.0
A6. In a sample of 400 shops taken in 2005, it was discovered that 136 of them sold carpets at below the list prices which had been recommended by manufacturers. What size sample would have to be taken in order to estimate the proportion to within 0.02? (Assuming 95% confidence)
(A) 2100
(B) 2260
(C) 2158
(D) 2156
A7. Given the following hypothesis: H0 : µ = 400 H1 : µ ≠ 400
For a random sample of 12 observations, the sample mean was 407 and the standard deviation 6. Using the 5% significance level, compute the value of test statistic.
(A) 5.03
(B) 6.23
(C) 4.04
(D) 2.98
A8. A researcher wishes to determine